The Use of Maths in Medicine

Maths is used every day in hospitals, surgeries and many more healthcare facilities around the world. As a prospective medical student, I wanted to know more about the huge role that this discipline plays in the world of medicine, and so I did some research and came up with the following conclusions.

One of the most basic and common use of maths in medicine is prescriptions and drug dosing. Most medications have guidelines for dosage amounts in mg/kg, and so doctors need to figure out how many milligrams of medication each patient will need, depending on their weight. There is a big role here for conversions, as sometimes patients will only know their weight in pounds or stone, and so this will have to be changed quickly by the doctor or nurse to the right units. This is extremely important as a wrong drug dosage could mean a life or death decision, especially if the drug being administered to the patient is especially potent and so could be toxic if given in high amounts, or if a patient is desperately in need of a drug, and not enough is given to that patient. Doctors must also determine how long a prescription will last, as this figure can be in days, weeks or months, and so healthcare professionals must be able to give the right amount of drug to a patient over a specific period of time, without the patient needing to come back as they don’t have enough of their medication.

Another important factor to consider is how long the medication needs to stay inside the patient.  This will determine how often the patient needs to take their medication in order to keep a sufficient amount of the medicine in the body. The amount of medicine in the body decreases by a certain amount in a specific time (e.g. 10%hour^-1), and this can be expressed as a rational number- 1/10. This rational constant creates a geometric sequence, as the amount decreases by a fixed ratio each time unit, and so doctors can use this concept to decide how often a patient needs to take their prescribed medication.

Another common use of maths in the medical field is for the calculation of one’s BMI, which is a number derived from an adults weight and height to judge whether they are of a healthy weight. This is a very common equation, used to test people’s weight all around the world, and shows that healthcare professionals have to be able to use equations with the right units; however, one’s BMI is not a very good indicator of healthy weight. I say this as, when you ‘plug’ weight into the equation to calculate a patient’s BMI, it doesn’t consider whether the weight is muscle or fat, and so a bodybuilder could be classified as ‘obese’ on the BMI scale even though they are healthy.

One of the more less-commonly known uses of maths in this field is through Extracorporeal Shockwave Lithotripsy, which is used to treat kidney and gallstones non-invasively. This technique is all thanks to the reflective properties of an ellipse, which can be seen in the diagram to the left. Shockwaves are generated at one focus and will reflect off the ellipse and pass through the second focus- creating a unique property which allows ESWL to take place. In order for the lithotripter to work, the patient’s stone must be at one focus point of the ellipsoid and the shockwave generator at the other focus.  The patient is then laid on the table and moved into position next to the lithotripter. Doctors then use a fluoroscopic x-ray machine to get a visual on the stone, allowing the focus to be at the precise location of the stone.  A water-filled cushion is then wrapped around the machine and rests on the patient’s side; this acts as a sort of buffer for the machine, as the water allows the shockwaves to travel through the body’s tissues safely because water and the soft tissue have the same density. The stone has a larger density and so is then shattered by the shockwaves. This is a popular choice for patients as it is quick, relatively safe and non-invasive, and so is available on the NHS.

In conclusion, mathematics plays a crucial role in medicine as it directly impacts people’s lives, and so it is very important for healthcare professionals to be very accurate in their mathematical calculations.

The Legacy of Elizabeth Blackwell

The World Health Organisation estimates there to be around 10-15 million practising doctors in the world; around 4-6 million of those being female. The figure is rapidly increasing, with estimates showing that females will soon outnumber male doctors towards 2017; however, this has not always been the case. Women have only been able to qualify as certified physicians as of the First World War, when doctors were desperately needed to take care of injured soldiers regardless of their gender, and one of the most influential women in this race for equality was Elizabeth Blackwell.

Born in Bristol in February 1821, Blackwell moved to the United States as a young girl with her family, where she first worked as a teacher, alongside her mother and two sisters. She had her so-called ‘eureka moment’ in her late-twenties, when Blackwell’s close friends was diagnosed with a terminal illness, and found it embarrassing to have male doctor. Compelled by a strong sense of compassion and determination, Blackwell then decided that she was going to peruse a career in medicine, although it was virtually impossible to achieve this feat. Her family told her it was a good idea, but unrealistic; it was too expensive, and such education was not available to women- yet Blackwell was strongly attracted to this challenge, and so applied to all the medical schools in New York and Philadelphia.

In 1847, she was then accepted into the Geneva Medical College after the male staff voted to let her join the university as a joke. As a determined young woman in an all-male medical school she was often humiliated by students, professors and patients alike; yet, she took this in her stride and graduated at the top of her class in 1849, after having written her thesis on Typhus fever.

She then worked as a physician in London and Paris, and her dreams of becoming a surgeon were shattered in 1851 when she contracted purulent opthalmia from a patient, leaving her blind in one eye.

However, after having encouraged many more women to become doctors, she opened a small dispensary in a rented room in New York, and this then further progressed into The New York Infirmary for Women and Children, which opened in 1857, with help from fellow female doctors Marie Zakrzewska and Emily Blackwell.  This institution and its medical school for women (which opened 1867) provided training and experience for women doctors and medical care for the poor, and is estimated to have helped at least 100,000 civilians in New York while it ran, and one of the alumni of the college (Sophia Jex-Blake) then returned to England and set up the first medical school especially for women in the UK.

In addition to this, at the outbreak of the American Civil War in 1861, she helped organize the Woman’s Central Association of Relief and the U.S. Sanitary Commission alongside President Abraham Lincoln, training nurses to help take care of injured soldiers in the war. After returning to England to continue her medical career in women’s medicine, she became the first woman to have her name placed on the British medical register, and published many papers and books, with some examples being: The Religion of Health (1871), Essays in Medical Sociology (1902) and most famously her autobiography- Pioneer Work in Opening the Medical Profession to Women (1895), in which she elaborately records her struggles and triumphs which she went through in being one of the first officially recognized female doctors in the world.

Blackwell showed the scientific world that women were just as capable of becoming eminent physicians as men, and in turn inspired a huge revolution of women in medicine and other scientific careers. It was from her inspiration and perseverance that we owe many female-specialized hospitals and health centres today, and in the words of the heroine herself: “If society will not admit of woman's free development, then society must be remodelled”.